Unpack the archive and make it. You will be told what else has to be done. Please note that we are not able to sort out any problems concerning the actual LP_SOLVE 2.x solver and that we are not responsible for that kind of problems resp. bugs.

Note that the bound constraints for the LP solver are derived from the current bounds of the real-interval variables. Further, when minimizing the objective function the following constraint is added. On the other hand, the constraint is added when maximizing.

This tutorial uses a multiknapsack problem to demonstrate the benefits of combining finite domain constraint programming and linear programming. First, we tackle the problem with finite domain constraints and linear programming separately (see Section 3.2 and Section 3.3). One difficulty arises for linear programming: since integral solutions are required and the LP solver returns non-integral solution, we have to implement a branch&bound solver to obtain an integral solution. Finally, we combine both solvers.

Throughout this tutorial, we use a multi-knapsack problem (taken from [BdB95]. The problem variables represent the number of goods to be produced. Each good requires certain resources: man power, materials, and machines (represented by matrix ) where a given capacity per resource () may not be exceeded. Each good generates a profit according to where the overall profit shall be maximal.